Rational Expressions, Vertical Asymptotes, and Holes.

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Presentation transcript:

Rational Expressions, Vertical Asymptotes, and Holes

Rational Expression It is the quotient of two polynomials. A rational function is a function defined by a rational expression. Examples: Not Rational:

Find the domain: Graph it:

Find the domain: Graph it:

Find the domain: Graph it:

Find the domain: Graph it:

Vertical Asymptote If x – a is a factor of the denominator of a rational function but not a factor of the numerator, then x = a is a vertical asymptote of the graph of the function.

Find the domain: Graph it using the graphing calculator. What do you see?

Find the domain: Graph it using the graphing calculator. What do you see?

Hole (in the graph) If x – b is a factor of both the numerator and denominator of a rational function, then there is a hole in the graph of the function where x = b, unless x = b is a vertical asymptote. The exact point of the hole can be found by plugging b into the function after it has been simplified.

Find the domain and identify vertical asymptotes & holes.

Horizontal Asymptotes & Graphing

Horizontal Asymptotes Degree of numerator = Degree of denominator Degree of numerator < Degree of denominator Degree of numerator > Degree of denominator Horizontal Asymptote:

Find all asymptotes & holes & then graph: